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On 3- and 9-regular overpartitions modulo powers of 3

Volume 154 / 2018

H. S. Sumanth Bharadwaj, B. Hemanthkumar, M. S. Mahadeva Naika Colloquium Mathematicum 154 (2018), 121-130 MSC: Primary 11P83. DOI: 10.4064/cm7317-10-2017 Published online: 6 August 2018

Abstract

Let $\overline { A}_3(n)$ and $\overline { A}_9(n)$ denote the number of 3- and 9-regular overpartitions of $n$. For each $\alpha \gt 0$, we obtain the generating functions for $\overline { A}_{3}(3^{2\alpha }n )$, $\overline { A}_{3}(3^{2\alpha -1}n )$ and $\overline { A}_{9} (3^{\alpha }n)$. We show that $\overline { A}_{3}(n)$ and $\overline { A}_{9}(n)$ satisfy certain internal congruences.

Authors

  • H. S. Sumanth BharadwajDepartment of Mathematics
    Bangalore University
    Central College Campus
    Bangalore-560 001, Karnataka, India
    e-mail
  • B. HemanthkumarDepartment of Mathematics
    M. S. Ramaiah University of Applied Sciences
    Peenya campus
    Bengaluru-560 058, Karnataka, India
    e-mail
  • M. S. Mahadeva NaikaDepartment of Mathematics
    Bangalore University
    Central College Campus
    Bangalore-560 001, Karnataka, India
    e-mail

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